> Which, I presume, means an object at thermal equilibrium emits and absorbs 
> equal amounts of radiation.

Yes, in a vacuum.  In air or with some other material contact, you need to 
include the conduction of heat too.

> OK. Well when I did some simple experiments at school, we found that a 
> glass of boiling water apporaches thermal equilibrium more or less 
> logarithmically. So I think we can safely conclude that thermal losses 
> increase at least linearly with temparature - even if the exact function 
> is hard to pin down.

Water is very stable thermally, for example it's specific heat varies by 
less than 1% from 0 to 100 degrees.  Other materials are far more unstable, 
and when you have several materials together in a system it is even more 
complex.  Then add in that your heat source may be generating different 
amounts of heat at different temperatures, and things are far from linear 
once you get away from simple science experiments.

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